A board member sold his home and moved from the neighborhood, yet he is still on the board.

I assume that you are referring to a member of an HOA board or something similar, since there are no residency requirements on most "boards", i.e. a member of IBM's board of directors can live anywhere.  It is likely that the person can be removed, but you have to look at your HOA rules.  Do they provide that board members must be residents, do they provide that they can remain on the board until the next election but can't run for reelection?  What do the rules provide?